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CMI-2019-DataScience-A: 6

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Let $R$ denote the set of real numbers and let $A=\{x\in R:x\neq 3\}$. For $x\in A$, let $f(x)=\frac{2x+1}{x-3}.$ Let $B$ denote the range of $f$. Then

  1. $B=\{x\in R:x \neq -2\} \;and \;f^{-1}(x)=\frac{3x-1}{x+2};$
  2. $B=\{x\in R:x \neq 2\}\; and\; f^{-1}(x)=\frac{3x+1}{x-2};$
  3. $B=\{x\in R:x \neq 2\}\; and\; f^{-1}(x)=\frac{3x-1}{x-2};$
  4. $f^{-1}(x)$ does not exist because $f$ is not injective.
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